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arXiv · 2509.14170

A Geometric View on Crossing-Symmetric Dispersion Relations

Joan Elias Miro·Andrea Guerrieri·Mehmet Asim Gumus·Ahmadullah Zahed
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Abstract

We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-t dispersion relations emerge as special cases. Within this setting we re-derive the null constraints from a geometric perspective. Finally, we present, for the first time, an explicit extension of Roy-like equations that remain valid at arbitrarily high energies, relying only on the rigorously established analyticity domain of scattering amplitudes.

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Joan Elias Miro, Andrea Guerrieri, Mehmet Asim Gumus, Ahmadullah Zahed. 2025-09-17. A Geometric View on Crossing-Symmetric Dispersion Relations. https://arxiv.org/abs/2509.14170

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